As one of the promising solutions for conveying high-bandwidth and low-latency services such as 5G, optical access networks face severe security challenges due to their tree-based topology and broadcast characteristics in downstream transmission. Even though physical-layer security mechanisms leverage the advantages of flexible implementation, low complexity, and full information confidentiality, these security enhancement schemes based on digital signal processing techniques are limited by the electrical bottleneck, leading to low processing speed for encryption and incapability of effectively detecting network attacks. In this article, we first discuss the potential security threats and present several existing solutions against security threats in optical access networks from the perspective of the medium access control and physical layers. We then elaborate novel optical-layer solutions based on optical signal processing techniques including all-optical encryption, optical layer authentication, and optical domain intrusion detection mechanisms. In particular, numerical simulation results have verified the feasibility and effectiveness of the proposed solutions. Finally, we conclude this article and propose future challenges of security enhancement of optical access networks supporting 5G and beyond.